This paper provides auxiliary results for our general scheme of computed tomography. In 3D parallel-beam geometry, we first demonstrate that the inverse Fourier transform in different coordinate systems leads to different reconstruction formulas and explain why the Radon formula cannot directly work with truncated projection data. Also, we introduce a gamma coordinate system, analyze its proper...

: Image compression may be lossy or lossless. Lossless compression is preferred for archival purposes and often for medical imaging, technical drawings, clip art, or comics. Lossy compression methods, especially when used at low bit rates, introduce compression artifacts. Lossy methods are especially suitable for natural images such as photographs in applications where minor (sometimes impercep...

Article history: Received 29 July 2008 Revised 29 May 2009 Accepted 3 June 2009 Available online 12 June 2009 Communicated by W.R. Madych A linear method for inverting noisy observations of the Radon transform is developed based on decomposition systems (needlets) with rapidly decaying elements induced by the Radon transform SVD basis. Upper bounds of the risk of the estimator are established i...

In image reconstruction there are techniques that use analytical formulae for the Radon transform to recover an image from a continuum of data. In practice, however, one has only discrete data available. Thus one often resorts to sampling and interpolation methods. This article presents one approach to the inversion of the Radon transform that uses a discrete set of samples which need not be co...

We develop an algorithm to reconstruct the wavelet coee-cients of an image from the Radon transform data. The proposed method uses the properties of wavelets to localize the Radon transform and can be used to reconstruct a local region of the cross section of a body, using almost completely local data which signiicantly reduces the amount of exposure and computations in X-ray tomography. For ex...

This work presents a new highly automated artificial vision inspection (AVI) tool for real-time defect detection and classification on circular knitting machines based on the combination of statistical analysis, Image Processing and Radon Transform. The tool (software + hardware) is directly attached to a circular knitting machine and the inspection is performed on-line. The automatic inspectio...

We examine the effects of the limited size, mean value and aspect ratio of datasets when applying the Radon Transform technique for the detection of alignments. We also introduce a Radon Transform equivalent to the Bartlett Periodogram approach, which has the advantage of improving the RT spectral estimates and can mitigate the aspect ratio problem. This technique is applied for the first time,...

Image Retrieval is very one of the biggest task in the recent years. It is widely used in many real time databases to retrieve related images in various fields like medical, military, online shopping etc. This paper offers with using radon transform followed by PCA and LPP techniques for image retrieval is called as Combined Radon Space Features Set (CRSFS). Caltech 101 database image sets used...

This paper investigates predictive coding methods to compress images represented in the Radon domain as a set of projections. Both the correlation within and between discrete Radon projections at similar angles can be exploited to achieve lossless compression. The discrete Radon projections investigated here are those used to define the Mojette Transform first presented by Guédon et al in 1995 ...